{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further Hypothesis Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──\n",
      "✔ ggplot2 3.3.0     ✔ purrr   0.3.4\n",
      "✔ tibble  3.0.1     ✔ dplyr   0.8.5\n",
      "✔ tidyr   1.1.0     ✔ stringr 1.4.0\n",
      "✔ readr   1.3.1     ✔ forcats 0.4.0\n",
      "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "✖ dplyr::filter() masks stats::filter()\n",
      "✖ dplyr::lag()    masks stats::lag()\n"
     ]
    }
   ],
   "source": [
    "# Select this cell and type Ctrl-Enter to execute the code below.\n",
    "\n",
    "library(tidyverse)\n",
    "\n",
    "set_plot_dimensions <- function(width_choice, height_choice) {\n",
    "    options(repr.plot.width=width_choice, repr.plot.height=height_choice)\n",
    "}\n",
    "\n",
    "cbPal <- c(\"#E69F00\", \"#56B4E9\", \"#009E73\", \"#F0E442\", \"#CC79A7\", \"#0072B2\", \"#D55E00\")\n",
    "\n",
    "set_plot_dimensions(5, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# You should see \"Attaching packages\" and some ticks by the packages loaded.\n",
    "# The \"Conflicts\" aren't a problem.\n",
    "\n",
    "# Other problems loading the library? Try running this cell.\n",
    "\n",
    "install.packages('tidyverse')\n",
    "\n",
    "library(tidyverse)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 - Testing for normality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsed with column specification:\n",
      "cols(\n",
      "  temperature = col_double(),\n",
      "  luminosity = col_double(),\n",
      "  radius = col_double(),\n",
      "  spectral_class = col_character(),\n",
      "  type = col_double()\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Run this cell to load the data.\n",
    "\n",
    "data <- read_csv(\"stars.csv\")\n",
    "\n",
    "type_key <- c('Brown Dwarf', 'Red Dwarf', 'White Dwarf', 'Main Sequence', 'Supergiant','Hypergiant')\n",
    "spectral_classes <- c('O','B','A','F','G','K','M')\n",
    "\n",
    "data$type <- factor(data$type)\n",
    "data$spectral_class <- factor(data$spectral_class, levels=spectral_classes)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Professor Xu thinks that the current system for classifying stars can be improved. In particular, she thinks that log(temperature) should be normally distributed for each star type. \n",
    "\n",
    "She has asked you to find out whether this is true under the current classification system, and if not, which types should be revised."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: for which star types is log(temperature) normally distributed?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-Q plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Theory\n",
    "\n",
    "We can use a Q-Q plot to investigate whether each sample resembles a normal distribution.\n",
    "\n",
    "If we set\n",
    "\n",
    "$x =$ the theoretical quantiles from the standard normal ($Z$) distribution, and\n",
    "\n",
    "$y =$ the quantiles from the sample,\n",
    "\n",
    "the Q-Q plot will be close to a straight line for samples that are approximately normally distributed.\n",
    "\n",
    "Although this is not a rigorous statistical method, it can be enough to suggest whether a normal approximation is likely to be valid for a particular data set, or to diagnose [*skewness*](https://en.wikipedia.org/wiki/Skewness) and/or [*kurtosis*](https://en.wikipedia.org/wiki/Kurtosis) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "do_plots <- function(sample, col='gray', lab='', mu='none', sigma='none'){\n",
    "\n",
    "    set_plot_dimensions(8, 4)\n",
    "    par(mfrow=c(1,2))\n",
    "    \n",
    "    # histogram\n",
    "    nbins <- 20\n",
    "    smin <- min(sample)\n",
    "    smax <- max(sample)\n",
    "    binwidth <- (smax - smin)/nbins\n",
    "    bins <- seq(smin,smax,binwidth)\n",
    "    hist(sample, breaks=bins, xlim=c(smin,smax), \n",
    "        xlab='observed', ylab='freq', col=col, main=lab)\n",
    "\n",
    "    \n",
    "    if(mu != 'none'){\n",
    "        n <- length(sample)\n",
    "        lines(bins, n * binwidth * dnorm(bins,mean=mu,sd=sigma), type='l', col='black')\n",
    "    }\n",
    "    \n",
    "    # Q-Q plot\n",
    "    \n",
    "    x <- seq(0,1,0.01)\n",
    "    normal_q <- qnorm(x)\n",
    "    sample_q <- quantile(sample,x)\n",
    "    \n",
    "    xlab <- 'standard normal'\n",
    "    ylab <- 'observed'\n",
    "    \n",
    "    # the plot itself:\n",
    "    plot(normal_q,sample_q, col=col, xlab=xlab, ylab=ylab, main=lab)\n",
    "    \n",
    "    # the line passing through Q25 and Q75:\n",
    "    m <- (sample_q[75] - sample_q[25])/(normal_q[75] - normal_q[25])\n",
    "    c <- sample_q[25] - normal_q[25] * m\n",
    "    lines(normal_q, m * normal_q + c, type='l', col='black')\n",
    "    \n",
    "}\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZZZACfbJ+rxKKCAAgoooIACCiiggAK5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      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### normally distributed data\n",
    "sample <- rnorm(mean=10, sd=2, n=100)\n",
    "\n",
    "### positively skewed data (e.g. lognormal)\n",
    "#sample <- rlnorm(meanlog=0.5, n=100)\n",
    "\n",
    "### negatively skewed data (e.g. constant - lognormal)\n",
    "#sample <- 20 - rlnorm(meanlog=0.5, n=100)\n",
    "\n",
    "### leptokurtic (heavy-tailed) data (e.g. Student's t-distribution with df=2)\n",
    "#sample <- 20 + rt(df=2, n=100)\n",
    "\n",
    "### platykurtic (thin-tailed) data (e.g. uniform distribution)\n",
    "#sample <- runif(min=10, max=20, n=100)\n",
    "\n",
    "do_plots(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can also be a useful way to identify the data points that are responsible for any deviations from normality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Application\n",
    "\n",
    "Run the code below to see the histograms and Q-Q plots for log(temperature) for each star type:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Brown Dwarf\"\n",
      "[1] \"mean: 7.99934325832345    SD: 0.116067269853234\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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2akmbNkX2Uq5lBCjvV6fG7zP9Ls2C1R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eP00+TfITcneJzmZzKrFJcquwP/ukW3cM\nAhDoBYGGjmRQP3SxuuDIrRp6sRs2LRCBb7WfvaUdpV8UaJ/spvQEVtMh3fr3pfSM9Ig0TfpY\n+pUUpz82+7WZ5C8shOaxMXzf4XdWM82+ryFNzVxRw8srqexPSOOkU6W1JZ93DAIQgAAEekGg\n2gNgo/GNn98tWscLndgtSp9fckuxg2YMAhDoHYF9/RTpvH0bg7q6ODZO9a5wFbq1HwIeK50v\nLVehZahltx00OhjyQ9rHpYukM6VrJb8T/EfpSikudqccmVdyl91dpBMk98r6j+RA+CdSaL4X\n+YvUT3pUqnXrKwCnS89Ln0o+9w6COyQMAhCAAAR6ScBPXLHZQTIcIACBwhDYWLvZpb4uSC7Q\nP0Hf58IwLdRe3MtlS+kGyV0p/T4pVhkELpCbfprkv69/ZLjsVlYHwAdIt0m3S+U2d7ffWtpJ\n2jTtzCfpNLdm+p10P3R+V/JvcVHpQcn+V7W9OaZh4/qgfi+dzaV1Sj8LUsn7pn3detOmo4N2\nFXwr6U9Ss+ReG+MlDAIQgAAECkigFlqAC4iLXUEAAt0QmEvrr5buVcMvrxJ0A6tMq3+u4y4i\nufUQqwwCfljtINEtqJnBr0swU/IYFh9KfsARB/M7vTtLu0pjpEOl1aWPJPdEuEoaKHm9W4od\nwDtYrlp79qCgcfK4Plc31NU/rI7gSyVSwasJXycTiQubkk0v9Gue9eDCXdytFSSC36r9NVAw\nCECgnARoAS4nfY4Ngeoj4JvYFulyya0/WPwIuBVuP+k+6YH0VBMsxgRcV1vvduGjWw/flubu\nIk85Vt2ug1pR+0ILIyQ/hF9KmiZVfffeeZdvPkdPBbdMJZPrDh7V9pzKbEss2D846uuW4KxF\n5k0M7PgsteG3bcE/Z6/ifwhAAAIQKAYBVz4YBCAAgUIQ2E07+Ym0r+QgGIsvAXc1HStdKfnz\nKli8CbiF10HRXlJ9J64urvQ1pGwtxJ1sUvZktxJPkao++J10ZrBkQgOVJZOp4ZHgd9YgVx9P\nD05pagh+d98xja0vn9HI+/ll/1niAAQgUO0EaAGu9jNM+SBQGgLuUnuxdKr0b8kD9WDxJnCS\n3PuxdKXk80WXdUGIkfWXL9E6+mgtPyzdKZ0svSS1SU3SppLfG71f+otUieYu3AdLHtzrz70o\nwMLa1t2rG3Pch69dRbdEU58t9Gm494eMmulz1Ff6jTRKck+MFb+YEUxTi8TARKJ+G51W+49B\nAAIQgECRCEQr1yIdgt1CAAI1QMBdnidKHrkUqwwCDp72kZ6XjpTOlbD4EHBL7qpZ3NlOaZZb\nT7+RHCiHtqBmHFSdGSZU0NQ9EVaRetsjYbr28bjkBwO5mN9LXj6XjL3Jk0wmByQSdR9oH50O\ncpVK1L0fJFLr9uY4bAsBCEAAAt0TIADunhE5IACBrgkcptUbS6tJfg8RqxwCb8nVw6WLpUel\nFyQsHgQelRtTe+BKT7bpwWEKvolbfj3o00e93LMfCpyWxz4OVN4d8sjfo6wvvN3+5eWPzXqg\n4QGu3Fp/kuRg/TtLJFIrqB/G298lMAMBCEAAAkUhQABcFKzsFAI1Q8Dvq50jHSU5mMIqj8CV\ncnlr6VppTcnvm2LlJ+BW+VoyB769DX7jyCshpw7a44/Js5ZfJNFw9p4NY4+9uf24TEffOrNp\nqNJ2SHYE22euYxkCEIAABApLgAC4sDzZGwRqiYCvHw6aHpHcgohVLoFD5LrfKT1bOqJyi1Ez\nni+lkrrb7nzSJ5K7sX8mxckGyhl3z34xTk6V2BcPcuVro7uy//a2Ixtm9GmoO3+3deunPvfP\nlkv2vGX24F/+LnBdXd11eg3/ziHHtnhkdgwCEIAABIpIgAC4iHDZNQSqnMBvVb6lpaJ3H6xy\njnEo3udyYoTkm++/pqeaYDEjsKL8cVdhv3IQNb/P7XS3GsdlMDMP1LWfdInkbvatUq1YXxXU\n18eR0qxBrjSdNvS4tmDSmGZ9+Cg4e831+/xu0nrBGzpdi+hbwAODVOrSjqkt5oRBAAIQgECR\nCRAAFxkwu4dAlRJYT+U6UdpD+rBKy1hrxXpIBT5PukJaWYpbi6JcqmlbQqV/WppLclDl97W/\nkJzuUbyPkPpJfqc1KcXFDpIja0mePhcXp4rox1bat9/xVaQb7C2Nl76zQaNa/vzquODmvqmm\nbZOJYOlEkPhMJ+uBwSNbPIggBgEIQAACJSBAAFwCyBwCAlVGYE6V5xrpaun2KitbrRfHDzW2\nlNxt0w83sPgQOF+u9JE2l/ywImr+RNK50mGSH2A8IcXFHPieLv1L8u9qnDRJqjZbSAXyAyT/\n3WQd5Cos8NCj/XCp9dpwmSkEIAABCJSWgD47h0EAAhDIi4BvYOulX+e1FZkrgUCLnPyptKM0\nvBIcriEfN1FZHUBmBr9G4C7Q7v7s94GHSXGym+WM34W9WzpU8mB590jbSdVwD+JBrn4pTZCW\nk9w75gjpByM8axmDAAQgAIGYEKiGyicmKHEDAjVBwCOU/kLyu33c4FXnKfdgWG4J/oO0tISV\nn8DccsEDXr3ShSv+BNkb0hpd5CnXKo/uvIvkhysOFLeR/K65g2H/1tyqvYhUaebA3q3tY6RT\npLWlZyUMAhCAAARiTIAAOMYnB9cgEDMCC8ifS6VzpDh1sYwZpqpwx638fl/zaol6ovyn9Eu5\nYK3WhStNWreCNKWLPOVedb0c8EBeG0n+bTno9Td7H5Telz6VDpLibn3l4BnS89J/JZfJXdA7\nJAwCEIAABGJOgBubmJ8g3INAjAj8Rb74JtWjm2LVTSCl4rkLtAfD+p9vllZ30WNbuvvkmQe4\n2j6Lh3432KNAD5AeybI+bkl+gObflwPg/SW/3/yANEOqhJbgf8jPfaW9pJ2kdyQMAhCAAAQq\nhEBDhfiJmxCAQHkJuNvzVtKaUlt5XeHoJSLgm3q/s3mVdL/k1i6sfAT8IMJ/g3dLDiBfkD6X\nlpC2kBaXbpXctbhSzK3aV2Q4WwkP5v2O78vS9AzfWYQABCAAgQogQABcAScJFyFQZgIDdXyP\nbnq89FqZfeHwpSVwgw63g3St5Icf30pYeQi8rcOuJPk1hK2lDaXQ3HLqnhl+PaHSTV8Fir09\nFXsPcRACEIAABDolUAlPWjt1nhUQgEDRCdTrCNdI/5I8KBJWewTcCtxPOrv2ih67Er8njzyA\nVH/JAy65O/RQyQNknSrNlOJiv5Qjc0lu5cUgAAEIQAACsSFAC3BsTgWOQCCWBNzt0gPrrCKl\nYukhThWbwBc6wAjJAxW5e627Q2PlJfC1Dv9seV3o9ugOxuMUkHfrMBkgAAEIQKA2CNACXBvn\nmVJCoCcE/DmV0ZJbAN+VsNol8LCK7lFu/b7mgNrFQMkhAAEIQAACEKh0AgTAlX4G8R8CxSEw\np3Z7vXSLdGNxDsFeK4zASfL3v9LFFeY37kIAAhCAAAQgAIHvCBAAf4eCGQhAIELgT5pvlA6J\npDFb2wRaVPyfSn7vdISEQQACEIAABCAAgYojUGsBcHflrdcZnFfyNxUxCNQqAX/fch9pb+mr\nWoVAubMS8KdfTpQ8INoyWXOQCAEIQAACEIAABGJMoLuAMMau5+zaQsp5k/SZ5Jv5R6QNpGy2\nshKdzwP/YBCoRQLLqtBu/T1eeqYWAVDmbgn4XWD/Nq6RaqEO6RYIGSAAAQhAAAIQqBwC1X7z\n0k+nwjdqe0pu3fVAPptIj0unSRgEIPA9gWbN+mGR/z4c5GAQyEbAo4EPl4ZKflCCQQACEIAA\nBCAAgYohUO0B8DE6E0tIv5MWl5aX/O3EVyR34xsnYRCAwGwCYzRZUHJw4yAHg0BnBPww0e+H\nj5YYFVoQMAhAAAIQgAAEKoNAQ2W42WMvf6QtP5Z+L7Wn9/KcphtLd0tHSR9I50iFtpW0w6Yc\nd+pupxgEikFgKe00lwBlmPI5oLGWTGtOTW3fzJ7k9f8g5U7ktUUMMqdSqUD/7Lc/AdUTW0Ab\nfdKTDbXNfD3cTj6Xxe835e/fpU06kjwv6em5YzsIQAACEIAABEpLoNoD4MWE8x9SGPyGdL/U\njEcy9bqzpLelm6VC2WDt6CWp4gKAQgFgP/EgUJcIXlJsMlce3lySR97uslZcVPT6+wokZz+4\n8oOyvE28g3LEguX2+6V3Ku5U531u2QACEIAABCAAgeogUO0BsAPbzSWP6jwz45R5QKxtpael\nq6T3pJ60dGmz/7GJSvH7x37vOBdbR5nckoJBoNAEmi8Y3hhsvFz2tx3aO1LB/pe2BfUK3C49\noDGodwSXtu3GtASrL10X/H53fw0pP7voofbg0kc78tsoBrnb5XJjfZB67tTm70Hk4dfqJ7Wk\nxDvRGe+udmXePbVy+r35GS3BVLV53/5sR7DLWrle8npaUraDAAQgAAEIQAACvSNQ7QHwQ8Kz\ntXS65Pcb35ei5qB3C8ktwfdIZ0uFshl57CifvHnslqwQCIK+il/79ckez435W7uCl1Rwz6jm\nYO45fpgnocUGxc2dbdsV26YKj4N6UuaQR1e8wzzZpubdWyuH3330osdKiyeCk25pC4ZquuzC\n2R+29LZsbA8BCEAAAhCAAAQKQaDa71QuEKTXJL/r+47k75pm2htK2FJKSr9PryzArWh6T0wg\nEFMCT77ZEfz54Y7gnH0ag4Xn4Scf09NUEW4NWTgRDFuhLjjkirbg65l0h66Ik4aTEIAABCAA\ngRolUO0BsLs9ryv9QZomtUrZ7D9KXEu6L9tK0iBQbQT+Oz0VHHVdWzBio/pgs6EV3lxbbSen\nQstz1t6NHkAsOP6mtgotAW5DAAIQgAAEIFALBKo9APY5/Fr6tbSMdIfUmU3Sim2kdaTbOstE\nOgQqnYBHDD5awe8icyeCY7ev9rcgKv1sVY7//dXN/k8jGoOHX0sGlz2WOe5g5ZQDTyEAAQhA\nAAIQqG4CtRAAR8+guzl3Z88ow8vdZWI9BCqVwMXq9vzC28ngD/s1Bk0NdH2u1PMYR7+XX7Qu\nOG2PxuCsu9uD56bkcrmNYynwCQIQgAAEIACBaiZQawFwNZ9LygaBbgm8MDUZjL23fVaQstT8\n/Pl3C4wMeRPwSNB7rFsf/Orq1sBd7TEIQAACEIAABCAQJwLcAcfpbOALBIpI4KtvU8ER17QF\nu61dH+y4Bu/9FhF1ze/6t7s0BAv0TwS/1u+toxwfRq75MwAACEAAAhCAAAQ6I0AA3BkZ0iFQ\nZQQ8OFFffbLmZAUnGASKSaBZXev9PvBr7yeDc9XjAIMABCAAAQhAAAJxIUAAHJczgR8QKCKB\na59sDx55PRn8Ue/99m3ivd8iombXaQKLz1cXjPtJ46xPbT30agdcIAABCEAAAhCAQCwIEADH\n4jTgBASKR+CdT1PB7+9sD367c0Ow3CL8yRePNHvOJLDpivXBIZvXByOvbwve+ZRBsTL5sAwB\nCEAAAhCAQOkJcDdceuYcEQIlI+Dvsv754fZg86F1wT7r0/W5ZOA50HcEjtqqIVh58brg0Cvb\ngpZ2BsX6DgwzEIAABCAAAQiUhQABcFmwc1AIlIaAwo2GdvU+PX3PxtIckKNAIINAXV0iOG/f\nxuDTr1PB6PG8D5yBh0UIQAACEIAABEpMgAC4xMA5HARKSGCUjlX3yx/XB3P15b3fEnLnUBkE\nBvRLBBcMbwpu+3dHcNszvA+cgYdFCEAAAhCAAARKSIAAuISwORQESkhgNx3rTIW97QMX5M+8\nhNw5VCcE1li6Ljhhx4bg/25tC17X6NAYBCAAAQhAAAIQKAcBXgosB3WOCYHiElhfu79WOjGR\nCE4p7qHYOwRyJ/DzjRuC56YkZ70PfNfR+iYXBoHCE1hQu7xYyvW9jyUK7wJ7hAAEIACBOBOg\naSjOZwffIJA/gUHa5E7pKuns/DdnCwgUl8BZezcG9ap5jrmhrbgHYu+1SuBbFfw16fUc9UGt\ngqLcEIAABGqVAC3AtXrmKXc1EhigQt0jPSsdVo0FpEyVT2DO5kRw0YjGYOfzWoO5+1Z+eShB\n7AhMl0cn5eHVgcq7VXf5Xx0dNPWdq/mgVCqxj14tGRgkUp9rkMEH2oOWc5Y7Onivu+1ZDwEI\nQAAC8SFAC3B8zgWeQKA3BJq18R3SDGlPiZGGBAGLJ4EhC9cFp+/RqAGxkoE+1cUIbfE8TXiV\nJjDpTD2r6d/nsSBIjE4lgkeTieRRqaS6WacSGzYGza9MGtOwIbAgAAEIQKByCBAAV865wlMI\ndEbAAcRV0lLSdtLXEgaBWBPYac36YJPlVsDKQAAAMSZJREFU6wJ/qivWjuJczRNINPW5JBWk\n5gq+nTl08NEzTxp8dOuNg0a1nH/N9Jnr6AHODUGi4fZXxwXz1TwoAEAAAhCoEAIEwBVyonAT\nAl0QOEPrtpEc/L7fRT5WQSBWBPZZv87Nv3wcOFZnBWeiBCad3TxEy3sGqeSIgScFH0XXjR4d\nJKdNbzkiCFJf9E02HRxdxzwEIAABCMSXAAFwfM8NnkEgFwIHKdPR0u7Sy7lsQB4IxIVAfV0i\n0EjlagTGIBBTAvWJjfQDnTZoVNsz2TzcdHTQrlbgO/VD3jjbetIgAAEIQCB+BAiA43dO8AgC\nuRLYWhkvlNzy8GCuG5EPAhCAAARyI5BIpObQi+pfdZU7Uef1CYZ06woS6yAAAQjEiAABcIxO\nBq5AIA8CqyrvzdKZ0uV5bEdWCEAAAhDIkYBGffbnlJZ96Yxg3k43SSXW1TvCzodBAAIQgEAF\nECAAroCThIsQyCCwuJb/Jt0l/SZjHYsQgAAEIFAgAtOmz3xM3fTfnbOp+bRsu5x4Tp8fa/02\nHcnkFdnWkwYBCEAAAvEjQAAcv3OCRxDoikB/rXTwO1Hav6uMrIMABCAAgd4R8Du+QXvHCI3W\ntv/kcX2ufPOMPgO9xwlnBf0nj20+rK4udZfeYh+77DFt/+rdkdgaAhCAAARKRYAAuFSkOQ4E\nek/An4u5VWqSdpFaJQwCEIAABIpIYOCx7f/o6EhuotGeV21oDiZNHtf8TVNj85d67/eUZBCc\nOHBkyzFFPDy7hgAEIACBAhPg+4sFBsruIFBEAn/Wvv3u7/rS50U8DruGAAQgAIEIgXQL7+pv\njGlaviGRGJhMdnze+k37c0NH8yAygolZCEAAAhVBgAC4Ik4TTkIgOFEM9pGGSVMkDAIQgAAE\nSkxguVGtE3RIC4MABCAAgQolQABcoScOt2uKwE9U2lOk3aSs36KsKRoUFgIQgAAEIAABCEAA\nAj0kwDvAPQTHZhAoEYFtdRyPLnq0dGeJjslhIAABCEAAAhCAAAQgUJUECICr8rRSqCohsL/K\n4aD3dOkPVVImigEBCEAAAhCAAAQgAIGyEaj2LtAHiuxcPaD7lLZ5ugfbsQkECkXgt9qRv/F7\nqPSXQu2U/UAAAhCAAAQgAAEIQKCWCVR7AOzgYbUenODR2qY3AfDS2v4fkj9Xk4vlfR4a64Ln\n9F3CgbnsPFueto7gHKW7ZRGLFwH/Fi6S/N7vzpK/+YtBAAIQgAAEIAABCEAAAgUgkHfgVYBj\nlnIX2+hg4yV/NsZdSS+XcrE3csnURZ53te4IqbGLPNFVQ7Tw+2hCd/MdqWDogcPqm1daPP9e\n7Nc82R78e1Jq2e6OwfqSE5hTR7xZWlsaJjHglSBgEIAABCAAAQhAAAIQKBSBag+APxSoTaXH\nJAfDv5NekIpt7TrA7XkcxAF63rbOwLpg0xXr897ukdc6gn8Hqby3Y4OiElhQe3dr7zySfw+T\nJAwCEIAABCAAAQhAAAIQKCCB/JsPC3jwEu2qRcf5RfpYfyzRMTkMBPIh4B4A7nKflH4kEfwK\nAgYBCEAAAhCAAAQgAIFCE6iFANjMXpVOlDwg1soSBoG4EFhXjnjQtdck91b4RMIgAAEIQAAC\nEIAABCAAgSIQqJUA2OjGSqtIL3sBg0AMCOwoHx6Wxkse8GqGhEEAAhCAAAQgAAEIQAACRSJQ\nSwFwkRCyWwj0iMDB2sqB75nSL6UOCYMABCAAAQhAAAIQgAAEikig2gfBKiI6dg2BHhPwiN/H\nSQdIV0oYBCAAAQhAAAIQgAAEIFACAgTAJYDMISCQJuDPYl0q7SptL90vYRCAAAQgAAEIQAAC\nEIBAiQgQAJcINIepeQL9ReBWaVVpE+l5CYMABCAAAQhAAAIQgAAESkiAALiEsDlUzRJYRCW/\nR+or+Ru/UyQMAhCAQC0T8Efsl5H+K31RyyAoOwQgAAEIlJYAg2CVljdHqz0CP1eRPfK4R3je\nQCL4FQQMAhCoCQILqpR/lq6IlHZuzV8kfSO9JX0qvSSNlDAIQAACEIBA0QnQAlx0xBygRgks\nr3L7xm8d6RRpjNQuYRCAAARqgcD8KqRf9VhMejxdYI+D4E+/rSElpUcltwD7Oulr5GDpMMnr\nMAhAAAIQgEBRCNACXBSs7LSGCTSr7KOlF6VvpaGSP3VE8CsIGAQgUDMETlRJHfyeIG2ZLvWv\nNHXw+xfJ6zaV9pCGSH+Q/Hm4zSQMAhCAAAQgUDQCBMBFQ8uOa5CAb+bclc/f9R0ubSPR5VkQ\nMAhAoOYIhOMdnK2St6RLv5Gmft/XrbwfptM8aZWOkt6RNpcwCEAAAhCAQNEIEAAXDS07riEC\n7up3pfR36RFpBelGCYMABCBQqwT8itULUrQ7c4eWp0ltUqY53/uSW4MxCEAAAhCAQNEIEAAX\nDS07rhECI1TOCdKakls33IWPEU0FAYMABGqawHMq/RbSgAiFxzW/rLRAJC2cXVgza0l+fQSD\nAAQgAAEIFI0AAXDR0LLjKiewnMrn1t4/SR68xe+1PSVhEIAABCAQBJcKgsdE+I/kh4O2yyQH\nxjdLi0qhraYZB8ceK2F8mMgUAhCAAAQgUAwCBMDFoMo+q5lAdJArv9e2knSmlK1LXzVzoGwQ\ngAAEuiLwrFa6R4xfEXlMcsvuBdLr0ibSVOk16SPJXaU9AvThkj8bh0EAAhCAAASKRsDv6GAQ\ngEBuBDzIlT9t5O9YjpB4z1cQMAhAAAKdELhC6fdIR0o/lfaT6iVbo+TxEvw9YF9LT5NekTAI\nQAACEIBAUQkQABcVLzuvEgKrqxwjpX2kv0jHS7znKwgYBCAAgW4IuIX3hLQc/Ppd38WkGdK7\nEtdSQcAgAAEIQKB0BAiAS8eaI1UWgTnk7l6Su/CtIz0q+T023vMVBAwCEIBADwh0aJv30urB\n5mwCAQhAAAIQ6D0BAuDeM2QP1UVgRRXnl5K76qWkq6Th0gQJgwAEIACB4hA4RLv1A8eLJL9q\n0lPzO8fnSU057mCZHPORDQIQgAAEqoQAAXCVnEiK0SsCvlHaXXLgu7H0tOR31m6SZkoYBCAA\nAQgUl8BC2v0qkqe9MQ9I+ImUawDcnD6Yt8MgAAEIQKAGCBAA18BJpoidEhikNQ56fy75Juha\nyaOQviRhEIAABCBQOgJu+fUnkPzOcG/sS218VB47WF95d8wjP1khAAEIQKDCCRAAV/gJxP28\nCfg375sdd7XbXPLnN06Srpe+ljAIQAACECg9AQe+vQ1+S+81R4QABCAAgYojQABccacMh3tA\nwCOPrirtLP1CmkfyZzfWlZ6RMAhAAAIQKCyBgdpdf8nf/8UgAAEIQAACsSFAABybU4EjBSTg\nd7/Wkvw+r7WBNJfkG7Ezpasld5PDIAABCECgOARO1m49mOAlkl8taZUwCEAAAhCAQNkJEACX\n/RTgQAEI9NU+1pPCgNfvdPmdXr/L+7h0qfQPyQOjYBCAAAQgUDoCB+lQfiDp6XOlOyxHggAE\nIAABCGQnQACcnQup8SbgbnVu1XXAu4nkm6s6yTdXDnjHSU9ItPIKAgYBCECgjAQc+J4u/Uu6\nWPL1eZKEQQACEIAABMpCoBYD4HlFem7JLYQe9OgL6RsJix8BB7oeqXlgeup5B7urSf5kxb+l\nhyV3tXta4jwKAgYBCEAgRgRuli93Sf6276HSIdJ90oXSvVJSwiAAAQhAAAIlI1ArAfDqInqY\n5NF/F8hCd7LS/i79n0Q32SyAipSU0H4XlaJBbhjsehqeKz+k8Dlyq8Ht0lGSg98WCYMABCAA\ngXgT8OjOu0g/kVzPbpOWr+uXSb6evyp9IGEQgAAEIACBohKohQD4tyL4uzTFaZq6pfAzya2/\nbgmeT1pScjet3aQjpOslrGcE/JtyK7u5RhWmza/0pSQHvctIfaSk9K7kmyEHuXem58Nlny8M\nAhCAAAQqm4DrVmtD6UBpD+k0KTRf60+QPHAWBgEIQAACECgKgWoPgF25Ovh1dyt/6/V5KZu5\nJXIjaax0nTRVekqqZnOZ3cW4r+QgNJ/pnMrv4DYMaqOBrvcZtRla8E1NVG9p+X7Jwa41VWKE\nUEHAIAABCNQAgSdURusIaVfJn6lbQVpRWkTCIAABCEAAAkUj4CComs3BrEcHdqWaS3dZB3Rv\nS35CfbDUU3NA6M/tNOW4A3f13VZqlnINBNv7NQf1DfVqPk0FQSqUduDlQJqV7tn0uuiykrsy\n76EjQ+1adkutZT8/lczUss/RaXTe+aO2shYmSt9GE3OcXyyd770c80ezOcAfIr0UTcxjviL9\nrksEP1tvcF39wu7rkKfd/3IyGNAvEay1TP6XidffTwVvfJBK7bymPOiB3fFcMiW/E/idG7xK\n5f3hl0Hwz4nJFl2b/BAOqy4CV6k4+0n+7rrOdM5Wp5yZ9UbOG/cg4/raxg+886l/e3AYNoEA\nBCBQ0QQc0/j+/kfS0xVdEjlf7S3Aq6RPkk9YLva5MjlACgOtXLYpRB7fHPxLyjX49THv/rol\nWFxTB6u+WfC0s/nM9QPSeT/QNAx0HeCG813dfDiQHCy9LFWamU8lWo/9VmDx0lNvJd3i3pMH\nDot/05IKpn2aercH0GY9cBj/bLKnDxxWwe+8qFcqbxfSDx0xCIQEuqp/wjxMIQABCEAAAhDo\nhMADSn9dauxkfWayW4C/ks7JXMEyBCAAAQhAAAI5E3CrfuYrMTlvXMKMbgH2Q8Zce2yV0DUO\nBQEIQCA2BHyN9LXS18yKN3c1qmZzF6zlpdukdbsoqLtpbiT5XeE5pDskDAIQgAAEIACBnhGY\nqc2m92xTtoIABCAAAQgUj0C1d4G+XugWlH4v7SD53VF35/xUckvvXNJ80lLSIpK7AY+UnpQw\nCEAAAhCAAAQgAAEIQAACEIBAxRHwN2VvkBwAu/k+qm+07Hckx0hLSBgEIAABCEAAArVBgC7Q\ntXGeKSUEINA7AlXVBbraW4DDUz1ZM/ukF9zq6zFx/X7Sx1I+o1MqOwYBCEAAAhCAAAQgAAEI\nQAAClUigVgLg6Llx12cLgwAEIAABCEAAAhCAAAQgAIEaIlDtg2DV0KmkqBCAAAQgAAEIQAAC\nEIAABCDQFYFabAHuikctreOTD7V0tikrBL4n4DEQ2r5fZA4CEBCBONSJvifzVykwCEAAAlEC\nrrc9UG85LQ7XyIKVnwC4YCgrakcPytvNK8pjnIUABApJ4BrtbL9C7pB9QaBCCYQPg/hkU4We\nQNyGAARKSqC1pEcr0sEIgIsENua7nST/fO5PjLmfubi3izLtIf0kl8wxz7Oa/PuT9KOY+5mL\ne/Mq098kDz73di4bxDyPvxF+hvRYzP3Mxb2LlGlKLhnJA4EaIPCsyri21Fjmsv5Ux99OOr3M\nfpT78LvKgcWkP5bbkTIff0T6+FeW2Y9yH/5wOeAvuIwvtyNlPr7v131PdV2Z/WjV8Z8rsw8F\nOTwBcEEwVtxO/AP+THq64jz/X4cdNH5bJWUJu5dUw3nx97dtL0qvz5qr7P/c9ehNqRrOjVu6\nwlavyj4reA+BwhBwEFxu8+eYXC//pdyOlPn4g3V8d/esdQ4bpM9DrXNwI8fL/B6Cg8XAX7Sp\nhnsQFaP8xiBY5T8HeAABCEAAAhCAAAQgAAEIQAACJSBAAFwCyBwCAhCAAAQgAAEIQAACEIAA\nBMpPgAC4/OcADyAAAQhAAAIQgAAEIAABCECgBAQIgEsAmUNAAAIQgAAEIAABCEAAAhCAQPkJ\nEACX/xzgAQQgAAEIQAACEIAABCAAAQiUgAABcAkgcwgIQAACEIAABCAAAQhAAAIQKD8BAuDy\nnwM8gAAEIAABCEAAAhCAAAQgAIESECAALgFkDgEBCEAAAhCAAAQgAAEIQAAC5SdAAFz+c4AH\nEIAABCAAAQhAAAIQgAAEIFACAg0lOAaHiB+BNrnUGj+3euSRy+HyVIO5HNVSlvb0CeF3Fr9f\nZjX9/cePLh5BoGcE+Luczc11RrXUGz37JXzPoTfbV8u2/F18/3uolvvDavltUo4KJDC3fF6g\nAv3O5nKzEpfItqIC0xLyeVAF+t2Zy4M7W1GB6cvI5/oK9Duby4socY5sK0iDAATKRqCPjrxY\n2Y4enwP3lysLxcedsnkyn45s1br5t+DfRK2brw2+RmAQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAgrgQScXUMv3Im4HO4dA6531eelhzyNSrPytJAaYr0gpSUSmGFKMt8\ncnTubpydofUfdZOnt6sLUZaoD320sKq0pPS29KKUy/lUtoJYIbn2lUerSAtIj0nTpXKZefr3\nbntZmjZrLvf/6pV1XWkR6SXpLalc1tuyRP1eWgsbSNdFE5mHAASKTsB17/KS6+IJ0htSLdvS\nKnwtXYviVKfE5Xe3sxxx3fpqXBwqoR9z6Fi+R1lKek96RfpSwiBQ8wT6i0AqB62TA6ntlefz\njH09q+UhOWxbiCyFKMvYDP+zsbmnEM52s49ClCU8xI81M1WKlmWKlp1eKisU153k8MdSWJZW\nzT8oLSyV0pp1sEslP9wJffH8JZIfNuRi/rt4XQq399QV9BJSKa0QZYn6O5cWXpPK+WAi6g/z\nEKgFAr4G3iFFryeef1hyUFyLVmvXorjUKXH6rR0oZ/x3MDJOTpXIl/10HDfWRK8JX2n5iBId\nv6oP01DVpauNwjmAOLeToi6o9J9KH0iTO8kTJu+gmTsl38DvL02VDpJ88RkvrSG1ScW0QpTl\ncTno1tdstqMSB0lPZFtZ4LRClMUuLSmZvy+Ax0l/k7aVjpdul1aVpkrFtkJw3UBO2ufPJF/Y\nn5RWl/4gOX2YVKpW7TN1rF9I90rnSknpaMm/95nSEVJX5t/YZdJi0r7SP6VNpfMl/75WlL6R\nSmG9LUvUx3m1cIO0gvR1dAXzEIBA0QjUac83SptIN0tXSjMkXyd/Lt0lrSX52lQrVmvXojjV\nKXH5je0kRy6MizMl9mMLHe9K6W3pROlu6cfSoZLvMz6XrpEwCEAgC4HblOaAYv0s6zKTnlHC\nV9KQjBU3adnB17CM9FIv5lOWbL6toUQH8HdKrmjKafmUZZQcNf9TMhwenU7/v4z0Ui/mw9W/\nMZdlwwwn19GyA9DzMtKLtejz79+6Wzjnjhykfzr9W027ezh4iPK4LL+UonagFrKlR/MUcr4Q\nZQn92UUzflXC/vu6QQuwIGAQKAGBTXQM/909leVYfujpdXtkWVetSbV4LYpLnRKH39QAOXGt\n5N+9H/p4OlKqJXtEhXW5t8wo9Nrp9Fcz0lmEAATSBPbR1H88o9PLXU020Urndatiprk752aS\nW5PLZfmUJZuPTUp8Sfqv5AtrOS3fsrh1z+fGrddR85NAp18YTSzxfD5cm+Vbu+Qu9dnsNSW+\nn21FEdL6aZ/25fks+35caeba3e/9X8rjinkeKWpzacEBtIP9UlghymI/t5Fcbv+N+LdmNgTA\ngoBBoAQEhusYU6QDshxrb6X5b/PkLOuqMalWr0VxqVPi8JsyC//m3RvCvSA8X0sBcJ3K+2/J\nQW69lGkTlOB7mGzrMvOyDIGaIrCwSvup9IbkwKM7O1oZfIFxa57NrWLurrqAF8ps+ZYlm7un\nK9Hl+3m2lSVM60lZ/PDBvo/P8POqdLoHhyiX5cN1aTnpcrj1O5u5C7HXu0txKewfOoiPt0rk\nYIM03yH9J5KWbbZRiS2SH6pksxeU6C7wzlcK601ZQv+20Myp0nzpBALgkAxTCJSXgLs/+lr1\ns/K6UbKj1+K1KG51SslOdicH+pPSN0+v21FT//5rKQBOFz3rpI9Sv5QmZl1LIgRqnEAYHO2Z\nI4dxyucLzDLS3ZKDAC9bDlgGSOWyfMuS6edgJfhJmZ+kJTJXlni5J2Wpl4+/k1wGj/7nFmEH\nJ+4yPFYqVZClQ/3A8uVqP90FPVtw6QcD4W9u5R8cpXgLPs7L0gzpWukyabrkSmVtqStz67D/\nNh7pJNND6fWLdrK+0Mm9KUtnvhAAd0aGdAiUjsD8OtQnkm94fZ2sRauFa1Hc6pQ4/c52lDOu\nb0fGyaky+nJymsdZZfSBQ0MglgTmlVfugunupLkGRzcpry8wrmhelH4h7SXdITn9SakcwWNP\nyiJXf2C+SLgMh/0gtfQLvSnLILnr1kaXI5QDtSFSuawnXB+Rs/Y/88GMK7awXD8qUYHcxSh8\nvzo8tqejJa/ryhz8O+8tnWRyuteX6vz0piydFIEu0J2BIR0CJSIwp44T9oxxnVyrVgsBcNzq\nlDj91giAvz8bvndyY8GbUt/vk5mDAARM4AgpvJHPlci96W1e09TdK6L2uBa8PwfEpbaelCXq\nox8AfCR9JfWPrijDfE/L4gveDOlpyS2Tviny9AnpG8nrS2095eqWSncd9gX8askB6DWSW14f\nk/w7W1UqtjXpAE9J9uUoacG0jtR0pvSoZM6d2eJaYV9v6yTD+PT6gZ2sL2Ryb8vSmS/Pa4XP\nCwYBCBSGgP9W58mibHt3y6+vUb7OnJ8tQwWn5cPBxayFa1Gc6pS4/bR2lEP+O6j1FuARYtAq\nfSitIGEQgEAGgZe17K6m+XS/vFz5fYE5TMo0D7nudedlrijBck/KEnVrNy3Y9wujiWWa72lZ\nHPh6YKLw3czQfb+n/b70YphQwmlvuK4uPz24g4Ng/04dyG8oXSr5XC0tFdu20gF8rJOzHOiY\n9LpdsqwLkxo04y7oj4QJGdNHtez9D8hIL8Zib8vSmU+1cNPZWdlJh0AxCOyrnfq6kKnMh87u\n8fNWOt/vNa02y5VDWO5auBbFqU4JucdlSgAcBL/VyfB1Y7K0bFxODH5AIE4E1pMz/iPxyHn5\n2CnK7O12z7KR/9i87ros64qZ1NOyRH26Twv2fWg0sQzzPS3LAvLVgeLtnfh8ldJdviU7WV+s\n5EJwdQurRzAO7WHNuEXbrcvFtj/qAOaWrbV5mfS6y7txwk9hO3v44O7qLkt9N/soxOpClCWb\nH7Vw05mt3KRBoFgENtWO784it4iGtpJm/GDTDwcPDBOrbJoLh2iRa+VaFJc6Jco+DvO1HAAn\ndALOl3y/4oaDhSSsQAT81AmrHgKbpYtyZ55Fej2dfw1Nb83YdpH08jMZ6cVe7GlZQr8cfAyT\nJkqvSuW0npbFwW+d5C662Sy8cXJZS2W94eqKzEH9ZZIDxNDc3W8D6UnJN37FtmT6ANm45srU\nfzNuubbvbqEPzeVz9yS33Pv8FdsKUZZi+8j+IQCB2T1GHukCxFpad7/kh4DbSQ9I1Whm0BWH\naixzLmWKS52Si6/kKT4B3/v5XmmE5PF4firNkDAIQCALgWuV5idF2Vq2smT/Lsk3/dOk96TF\nvkudPXOLJt7nmhnpxV7saVlCvwZrxn531noa5ivFtDdlcfDu9z58cxQ1n6cvpHejiSWY7w1X\nP1zxOdkow89ztOxgceOM9GIt7qEd2w/740omamO04HXdtb7sms53bHRjzR+fTt89I71Yi4Uo\nSzbfaqXVJVvZSYNAqQl4QJsp0kxp/VIfPObHq5VrUVzqlLj9HGq1BfgQnQjfi4yXStnIEbfz\njz8QyImAK4p2qbmL3Ktonf+oMrtvDleaW5Nekw6WtpSuk5zXAUqprTdlsa87Svb9VC+U2XIp\ni10cL9nnXbyQNgeLDg4/k46T3H3sAOltyXm3lUppuXLNVpZN5Kh/n29Kh0vbS5dLLsfvpVKZ\nuxW5pcXHvUvaS9paulRy2lNStMLJVhYHzv5b8bnxb2xzyWXwsvOXyvItyypyzGXM/PvP9Pd5\nJUzPTGQZAhAoCoFTtFf/XfohtFt7ssnX/Vq0WrkWxaVOidtvbEc55L+NkXFzrIj+DNC+P5dc\n7oekbNcDp/WTMAjUPAFfPN09wt1ourKuboAdTIWBlf/w3pfOlnyTXUorRFnCljgHN+W0XMti\nH8dL5h4NgJ2+kfSy5HWh3tD8FlKpLVeunZVlbzn8gRSWwy0ef5QapFLanDqYH+y0SKEvbmm/\nUJpbilpnZXH353slPzgK9+HAemGplJZPWbr6+4/6/LwWpkcTmIcABIpG4AXtObyGdDY9v2hH\nj/eOa+laFJc6JU6/iB3Tfxsj4+RUkX3ZKV3mzq4FYfq8RfaD3UOg5gj4Bn75mit1/As8QC6u\nKS0Qf1e79NDB7rLSqpKDt3KaffFvfUWpsYeO+BNbPi+lDnwz3S1EWTL3yTIEIAABCJSWQFzq\nlNKWmqNBAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABKqQQH0VlokiQaAaCcytQm0rNUofV2MB8yiTGewkzSW9l8d2ZIUABCAA\nAQj0hsAq2vhH0vtSS292lOO21Hffg5pXs9tIjl0++T6ZOQhAAAIQqFYCq6lgKem8ai1gHuVy\nJWgWt+WxDVkhAAEIQKByCawk16+LgfvnywfXPyuXyBfqu+9Br5dmf9b3ScxBoGcEGnq2GVtB\nAAIQgAAEIAABCECgJARu11H6lORIHAQCEKh6AnVVX0IKCAEIQAACEIAABCAAAQhAAAIQEAFa\ngPkZQKD8BJrkwq5S2KXqRc3/VZohZbMFlOj8Q6SXpXukbO/DLKL03aVBkt8bflX6m9QuZZr3\n9WNpOWmq9Kj0khQ1r3d3rLul/aUB0sPSstLb0qNSpq2vBK/3Np+lV/q6s53kbt3N0n8kr/9W\nymbe3u8/zyP5eC9LGAQgAAEIVD6BhIqwteTurf2kCdJj0puSzWM97JKe+n3Y4dIU6XEptA00\n4/pksOR6xtveKc2UQhumGdedt0hrSMOkhSTXP+OlbO/z9lW6672NpTck11Od2fxasZnkOtR1\n1UTpCSlajw7Q8vbSk5LLuof0gnSv9I1k6019N0zb51vGodpmC2kpKeRqJlEzg8y633xfkYZJ\nLvut0tqSGbiOf0RyOW1m4nO8hPSsdJOUkqKWC79ofuYhAAEIQKCCCawu39+SXBl8JX2Znnfa\nOlJortyd5+/SO1Kr9JHktA+kjaSoba4FV/5e/1/Jlbvnn5EWk6I2Ugten5S8bwfIHdJpkm9O\nQnPl70D3Asn7sh6U3pc+lOqlTHM5HHw3plcM1PRfkrd1We2b51+TVpEy7UIleL3L+0l6/tL0\nlHeABQKDAAQgUKEEXC84+PM13vVOWKe5PvqVZBsiuW5yHsvzN0g2Dw55sxSmh3WElx2wLiqF\n5iDXddXRkvfRJoX7fF7z80lRcyD6ueQ8rsOcf5r0gOS08IG1ZmcNyhge2/VaWPe6Hj3WGdK2\npqbe1nXrF+l5L28g2Xpb3+VbxnE6prmbh9l4ap+d7iA2tM7qfq/3MX3f8BvJZXFd7al1iLSL\n5PMZTQ/Pn5Jn2U76Pxd+6ymf93vWrK34DwIQgAAEKpJAX3k9Qfpa2luqkxxw7io5GH5Pmkuy\nhQGwL/7XS3M6UbaZ5EraAegcUmiTNeMKZcV0Qj9NXel6+zPTaZ7sIDnNT9zDm4X+mvcxnD5c\nCs2VoCtLH+8AaR9pY8n7c96tpKitrwWnuzK1uWzPSK5gf5Ze1mTW0+dPNfUNS5MT0uZjePtr\npLBsLq/zOv02CYMABCAAgcoksJ/c9rX8bMn1js11loMx9wiaRwrND1MdaEVttBa8/XmSWxBt\nK0i3SE53nReaAzUHeB9LB0vzSgtLf5Wc9wQpNPvih7Kua4ZJNteh10rOa60s2VxHu7523rWk\nesn1885SizRDmluyhQGwg+lbpW2lkZKtEPVdPmXcX8d0Oe6T3BJuM8O7JKeHfml2Vst3trrf\n68JjTte87wEapS0lPwhw+T+TDpd8LpeW3pS8f58nWz781lN+b0sAbHIYBCAAgQolcJT89sXc\nT04z7WgleN3J6RWrpZd9A9CcTgsnx6TXuZKx9ZEcZD4qOegMzdu5kt8mTNB0guTjuGKOmitw\nV9y+EQn3cbfmnTd8Mq/ZWbac/nf6NbMXv/v/T+n08EZh7/Sy95NppyjB+/hlZIXL+qHUN5Lm\n2SMk573NCxgEIAABCFQkgfCh7KYZ3juAOkwKAzOvzhYAO/B9QJrDGSLm+sx1hIPM0ByoZdYx\nXueA2+leH9ovNOM019FRcx3qOtHrwnrNQdl9krfJtLDOXCm9IvTrXS17X1ErRH2Xaxldp/tB\n9qdSGJyHvrju/0CaLnneFpYjs+73uvCYPl9RCx8suG6P2v9pwfx2SSfmw895vS0BcBoek54T\nqOv5pmwJAQj0ksCq6e2vy7IfP2m2+Yly1O7Qgp+qRu329EKYd6aWn5Q2kZ6SXImvIHm7MyR3\nObP5iexykm8s/ER6lYgGaf4ZaREpbBnW7Cz7VziTnr6h6dOSK7SwwmzS/F7Sc9LLks2Vl+1h\nKXosz/tpuy0swwDNLy755uZbKWo3RReYhwAEIACBiiTwUNprtzr6gekOkusQX/fdHfgjqSs7\nUisdLPthrW1+aUNpOy/IMgNjp7lOjNrU9MJckcSwbr4zkuZZ16GZaf9U2tbSZZLNLaDLS3tL\nYQCf6ceLWud9hVbo+q67Mi6lA7v+/5v0ZehEevqNpr6n6Ce5HFHLrPuj61zXRy2s9/8dTdS8\ng2tb/9mToCf80psygUDPCTT0fFO2hAAEeknAwaefZvrJb6Z9rAQHfoMzVrydsexFP022DZw9\nmfX/7vr/RslP1h14jpOmSFdLp0ut0hDJ5qkr5M7MPrwXWen9ZNrlSviLtJN0vbStNJ/0Wym0\n8Hj2pTMLy7tyOkP0uOE2ZhO9eQjTmUIAAhCAQOUQ8MPQA6Sx0iFp+dr+d+lUqauAS6tnvTa0\nr6YjJNcZDiRtn8+efNd7Kb04a/JhdEHzfmBsizYI+aGsLVv9M232qh/873prpDRM8nyDlJSm\nSza3uEYtsw4tdH3XXRl972HLdj8RTXdZnnNC2jL9DtM9zdyXe6HZvpg9+e7/MP27BM3kyy+6\nLfMQ6BEB/5FiEIBAeQj4Sasrxr6SW2Cj1qSFPlJYOYfrnJ5pYavrfyMrHCT+WFpW2kbaWhom\nnSytL20lhfu+X/PnSJ3ZKxkrHDxn2k1KOF/6meQA2DclvpG5QQotPN5PlfBRmJgx/Sq9/Gl6\nGpYtms3M6qIJzEMAAhCAQEUSuExeXydtLrlecn3lFtwt0suPatqZXaAVh0iTpZulZyQ/zH1f\n+kDKZg5Mu7No/eN6LGr10QXNLy89JfWXXJdeI/1Hsi+jpUOlTMusQ6PHy8zbk/quuzL63sOW\nrX51ustiC+vs2UuzH5yH85nTzDJlru9suSf8OtsX6RDImQABcM6oyAiBghN4S3vcTFpR+mfG\n3l0puOJ7OyN9cMayF729beLsyaxKbXXNfyK9Ib0pOTj103HfHGwpLSo5f0pyt7GHpExbVwl+\nWhs+xc5cH112nlulfaSlpO0kd2v7TArNftgc5GYez92x1pI+lGzuEu0WcHPINO+/MTORZQhA\nAAIQqCgCrs+Wle6R/pqWJsFx0pmS65NHpWy2oBId/LqucN3h+iK0DdIzmcFquL676XPKsKvk\n+sfBbdSGRBc0f4Q0rzRCukqKmstm686PUtd3vvewhfcOs5e+/z9Mz7z/+D5H4eYKwa9w3rCn\nmiFAK0rNnGoKGkMCd6R9OkFTB7tROzG94HdxorazFpaIJmj+WMmB7M3pdN9U/EO6Nr0cTvyU\n2RWag1o/2fUNwwPSmtK2UtSGauFx6TLJ+87FrlAmB6YXS82Sl6PmgNj7ctkybwguUNqD0vqS\nzT4+KW0urSFFzRUmBgEIQAAClU3gHLnv91D9wDRqz6cXZkQS2zQ/Z2R5mfS8exNFg1/XpQ6M\nbT19UOq6z+a6NWqLamH3aILmQz+mZKT7IXRYn3XnR6nrOzP7p7Sl5IcHUVtJCztKLo8fmBfb\nCsGv2D6yfwhAAAIQKDCB8dqfg8K/SrtIfoc2TLtE867MbatJzueWVj+9PUDyTUOY9wrNR+1h\nLTi/g+zh0p7S1ZLTbpNCW04zvnmwTpa2kFzpu3W4XYpWjndr2dvPJWUz+zpJcp73pMwgV0nB\n5ZLXPyHtJbnMV0lOu1OK2hJacDc2B+6HSq6sL5R8U2TfouXQIgYBCEAAAhVEYFP56uDvXek0\naWvJD4Rd//gh7dpSaI9qxvXEFdL+0hzSx5LTfi852HSd4ofG7uLrOi0awIV15QClR61OC96H\n68yo2R+nu2eTHxDvJ02WXAc7fWXJdozk5eekfaQfScdJn0iuu7zO9ZxtTcnL47yQYYWo7/Ip\no31plb6QRkqbSb+W7LO1qhTa3Zqx39nq/s6O6XPibTaUojZCC043T1s+/NZTfm97ljfEIAAB\nCECgcgk0yvVTpK8lX9gtV/6nS2Hwq9nvAmBXrNdJvmlwXlfyrqgzg80BSrtecqAY7tddjy+Q\nfMyouZvX41K4T+f3DclwKWpdVYJhvt9oxtufESZkTH2z4QrPlW7oV1LzvslYWMo0B+APSa6o\nnf9DaRNpunSbhEEAAhCAQOUS2EuuT5Wi9cGrWl5Xipqv+265dL5X0iscXPmBcLit6zvXU0un\np67TFpVsnQVqnQXArn/PlN6RvH/v23WvA3QvryzZXPdeJEXrWtdTB0quv5z3z5JtTcnL47yQ\nxXpb3+VbxtXlw7OSfbL8cPnvUmavq67q/s6OmWsAnA8/AmCdHAwCEIBANRFwZTtIWiLHQvVX\nPndVaugmfz+tHyoNkaIBdbbN/ETdLc1LSa6Uim1L6gB+yjxXDgeaW3lcBgwCEIAABKqLgIPQ\nxSUHXt3VBwspTx8pNG+7tLSKFE3XYsFsee3JdW5XZr9df4YBd1d5u1tX6vrOvptfU3eOFXF9\nIfkV0U12DQEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAESkXg/wGns0dZBZxw1wAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Brown Dwarf”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Set the star type to test\n",
    "t <- 0\n",
    "\n",
    "sample <- data %>%\n",
    "    filter(type == t) %>%\n",
    "    pull(temperature) %>%\n",
    "    log\n",
    "col <- cbPal[t+1]\n",
    "lab <- type_key[t+1]\n",
    "\n",
    "mu <- mean(sample)\n",
    "sigma <- sd(sample)\n",
    "\n",
    "do_plots(sample,col,lab,mu,sigma)\n",
    "print(type_key[t+1])\n",
    "print(paste('mean:', mu, '   SD:', sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For which of the star types does log(temperature) appear approximately normal? How would you describe the other distributions?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, for a more rigorous investigation of normality, we can use a statistical test:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shapiro-Wilk test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Theory\n",
    "\n",
    "The [*Shapiro–Wilk test*](https://en.wikipedia.org/wiki/Shapiro–Wilk_test) tests the null hypothesis that a sample $x_1, ..., x_n$ came from a normally distributed population.\n",
    "\n",
    "It compares statistics obtained from the observed data to the expected values of statistics sampled from the standard normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Application"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Shapiro-Wilk test is easy to apply in R:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Brown Dwarf\"\n",
      "[1] \"p = 0.00215765989350542\"\n"
     ]
    }
   ],
   "source": [
    "### set the star type to test\n",
    "t <- 0\n",
    "\n",
    "sample <- data %>%\n",
    "    filter(type == t) %>%\n",
    "    pull(temperature) %>%\n",
    "    log\n",
    "\n",
    "p_value <- shapiro.test(sample)$p.value\n",
    "\n",
    "print(type_key[t+1])\n",
    "print(paste('p =', p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apply the Shapiro-Wilk test to each of the star types. Which of them produce p-values less than $\\alpha$ = 0.05? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Alternative tests for normality\n",
    "\n",
    "Many other tests for normality have been developed, including the Anderson-Darling, Cramér–von Mises and Kolmogorov-Smirnov (see below) tests. \n",
    "\n",
    "The Shapiro-Wilk test has been found to have the best statistical power for a given significance level.\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
